Target and technical efficiency in DEA: controlling for environmental characteristics

In this paper we propose a target efficiency DEA model that allows for the inclusion of environmental variables in a one stage model while maintaining a high degree of discrimination power. The model estimates the impact of managerial and environmental factors on efficiency simultaneously. A decomposition of the overall technical efficiency into two components, target efficiency and environmental efficiency, is derived. Estimation of target efficiency scores requires the solution of a single large non-linear optimization problem and provides both a joint estimation of target efficiency scores from all DMUs and an estimation of a common scalar expressing the environmental impact on efficiency for each environmental factor. We argue that if the indices on environmental conditions are constructed as the percentage of output with certain attributes present, then it is reasonable to let all reference DMUs characterized by a composed fraction lower than the fraction of output possessing the attribute of the evaluated DMU enter as potential dominators. It is shown that this requirement transforms the cone-ratio constraints on intensity variables in the BM-model (Banker and Morey 1986) into endogenous handicap functions on outputs. Furthermore, a priori information or general agreements on allowable handicap values can be incorporated into the model along the same lines as specifications of assurance regions in standard DEA.

The cost of Corporate Social Responsibility: the case of the Community Reinvestment Act

A Data Envelopment Analysis (DEA) cost minimization model is employed to estimate the cost to thrift institutions of achieving a rating of ‘outstanding’ under the anti-redlining Community Reinvestment Act, which is viewed as an act of voluntary Corporate Social Responsibility (CSR). There is no difference in overall cost efficiency between ‘outstanding’ and minimally compliant ‘satisfactory’ thrifts. However, the sources of cost inefficiency do differ, and an ‘outstanding’ rating involves annual extra cost of $6.547 million or, 1.2% of total costs. This added cost is the shadow price of CSR since it is not an explicit output or input in the DEA cost model. Before and after-tax rates of return are the same for the ‘outstanding’ and ‘satisfactory’ thrifts, which implies a recoupment of the extra cost. The findings are consistent with CSR as a management choice based on balancing marginal cost and marginal revenue. An incidental finding is that larger thrifts are less efficient.

Estimating DEA technical and allocative inefficiency using aggregate cost or revenue data

In this paper, we address the question of Data Envelopment Analysis (DEA) evaluation of efficiency when aggregate cost or revenue data must be used. We show that the DEA technical inefficiency measure using total revenues as the single output variable or total costs as the single input variable equals the aggregate technical and allocative inefficiency. We employ this result to estimate allocative inefficiency and construct statistical tests of the null hypothesis of no allocative inefficiency analogous to those of the null hypothesis of no scale inefficiency. We illustrate our method using revenue and personnel data for the top U.S. public accounting firms over 1995–1998. Our empirical results indicate the existence of statistically significant allocative inefficiency in the public accounting industry.

Efficient frontier estimation: a maximum entropy approach

An alternative efficiency estimation approach is developed utilizing generalized maximum entropy (GME). GME combines the strengths of both SFA and DEA, allowing for the estimation of a frontier that is stochastic, without making an ad hoc assumption about the distribution of the efficiency component. GME results approach SFA results as the one-sided inefficiency bounds used by GME shrink. Results similar to DEA are achieved as the bounds increase. The GME results are distributed like DEA, but yield virtually the same rankings as SFA. The results suggest that GME may provide a link between various estimators of efficiency.

Production technologies based on combined proportionality assumptions

The assumption of full proportionality is incorporated in the constant returns-to-scale (CRS) technology and allows for proportional scaling of inputs and outputs of production units. The assumption of selective proportionality was recently incorporated in the hybrid returns-to-scale (HRS) technology in which only a subset of outputs is proportional to a subset of inputs. In this paper we develop a production technology that exhibits both the full and selective proportionality at the same time. Real examples of such technology are pointed out. Subject to certain conditions, the DEA models based on this technology provide better discrimination than the CRS and HRS models.

Public inputs and dynamic producer behavior: endogenous growth in U.S. agriculture

This paper is an attempt to understand the impact of public R&D and public infrastructure on the performance of the U.S. agricultural sector during the last part of the twentieth century. A neoclassical Solow growth model is not sufficient for this understanding given the sustained growth performance of the sector. We base our analysis on a well-known endogenous growth model, the ‘AK model’ where non-convexities are introduced through non-rival inputs. Based on these models and within the dynamic models that rationalize private and public decision making, we have identified three testable hypotheses regarding the aggregate agricultural production technology. They are: (1) increasing returns to scale over all inputs; (2) positive effect of additional units of public inputs on the long-run demand for private capital; and (3) negative impact of public inputs on cost. They are tested using two estimation procedures on two data sets for U.S. agriculture. One, covering the period 1948–1994, developed by USDA, the other, covering the period 1926–1990, from Thirtle et al. Maximum likelihood estimates do not conform to the regularity and behavioral properties of the economic model rendering them unusable for testing these hypotheses. Bayesian estimates, although not totally satisfactory, do not reject the hypotheses after prior imposition of some of the regularity conditions. This supports the notion of an important role for public inputs on the rapid and sustained growth of the sector. We calculate that, on average, one additional dollar spent on public R&D stock reduces private cost by $6.5, implying a return on these public expenses of 190%.

A response to the critiques of DEA by Dmitruk and Koshevoy, and Bol

We here critique the articles by Dmitruk & Koshevoy (1991, J Econ Theory 55:121–144) and by Bol (1986, J Econ Theory 38:380–385) by showing how to solve the examples they erected to show the non-existence of functions for evaluating performance efficiencies in DEA. We also show that functions satisfying these criteria—and other important criteria as well—were already available prior to the publications of D&K and by Bol and have since been greatly extended to increase the power and scope of DEA.

The cost of strikes in the Spanish mining sector: modelling an undesirable input with a distance function

In some contexts, firms have to deal with certain elements or factors that affect the production outcome but which are non-market in nature and therefore do not have a price. In this paper we propose a new use of a production economics tool, the input distance function, to empirically measure the effects of these factors. Although we suggest a general use of this methodology, it has been developed in the context of measuring the effects of labor disputes in a particular declining industry, that of Spanish coal mining. We have estimated an equation system comprising an input distance function and cost share equations to calculate the cost generated by strikes.

Financial liberalization and banking efficiency: evidence from Turkey

This paper examines the banking efficiency in a pre- and post-liberalization environment by drawing on the Turkish experience by using DEA. The paper also investigates the scale effect on efficiency. Our findings suggest that liberalization programs were followed by an observable decline in efficiency. Another finding of the study is that the Turkish banking system had a serious scale problem during the study period. The second part of our analysis relied on econometric methods and found that one major reason for such system-wide efficiency decline has been the growing macroeconomic instability of the Turkish economy in general and financial sector in particular.

Joint estimation of technical efficiency and production risk for multi-output banks under a panel data cost frontier model

This article generalizes production risk from a single output production function to a multiple output cost frontier, which is able to examine input-oriented technical efficiencies and production risk simultaneously in the context of a panel data. Furthermore, the joint confidence interval estimates for technical efficiencies are constructed by means of multiple comparisons with the best approach. Whether taking production risk into account or not offers quite dissimilar implications in terms of the average technical efficiency measure and the identification of multiple efficient banks achieving the optimal cost frontier. It is suggested that inferences drawn on the basis of the confidence intervals of technical efficiency provide much more fruitful and insightful information than the point estimation alone. Bank specific risk parameters are found to be highly and positively correlated with fixed-effect estimates, implying that the more risk-averse a bank is, the more technically efficient it will be.

Productivity efficiencies in Ukrainian polyclinics: lessons for health system transitions from differential responses to market changes

Ukraine’s recent elections revealed deep divisions between eastern regions, which favored central economic planning, and western regions, which preferred more free market reforms. This study compares polyclinics in Ukraine to see if the inflexibility of Soviet-style planned economies results in lower economic efficiency in eastern regions. Using data from two geopolitical regions, Data Envelopment Analysis (DEA) scores for polyclinic efficiencies are modeled as a function of demographic and economic determinants. Surprisingly, results indicate that polyclinics in western Ukraine are less efficient. Possible explanations, including case mix intensity, responsiveness to local preferences, physician entrepreneurial behavior and a legacy of inequitable funding, are discussed.

Economic assumptions and choice of functional forms: comparison of top down and bottom up approaches

Two alternative model building approaches are analyzed and compared. The general to specific modeling (top down approach) starts with a general model and subjects it to a sequence of restrictions to determine an acceptable specific model. This approach can start with a series expansion and the concavity or homotheticity conditions can be imposed to modify it into a cost or a production function. The simple to general modeling (bottom up approach) starts with a well known simple model and extends it until a complete system is formed. This approach can start with a Cobb-Douglas function (which satisfies the concavity and homogeneity conditions) and extends it to include the desired complexity. Relative advantages and disadvantages of the two approaches are discussed and tabulated. The electricity generation data is applied to compare the performance of these two approaches.

Measuring performance in the presence of stochastic demand for hospital services: an analysis of Belgian general care hospitals

Since demand for hospital services is subject to substantial variability, the relationship between uncertain demand, excess capacity, hospital costs and performance should be investigated thoroughly. In this paper a waiting time indicator to proxy hospital standby capacity is incorporated into a multi-product translog cost function for Belgian general care hospitals. The indicator is derived from queuing theory and improves on the conventionally used (inverse of the) occupancy rate. The multi-product stochastic frontier specification allows calculation of cost elasticities and marginal cost of seven hospital departments, as well as the degree of economies of scale and scope and enables identification of differences in efficiency.

A generalized procedure to recover the first derivatives of a production function when the firm is a profit maximizer

Partial derivatives of production functions are necessary in many instances to characterize the technology of firms. We present here a general method to recover the first derivatives of the production function of a profit maximizing firm. The method is systematic and applies even when the optimization problem of the firm is subject to additional constraints. It allows researcher to recover returns to scale and technological progress in complex situations.

The productivity performance of Irish dairy farms 1984–2000: a multiple output distance function approach

This study measures productivity growth on Irish dairy farms over the period 1984–2000. A total factor productivity index is constructed for the dairy system and is decomposed into technical change, efficiency change, and changes in scale efficiency. This is achieved by estimating a stochastic output distance function model of the production technology in use on Irish dairy farms. Overall, productivity on Irish dairy farms grew by 1.2% per annum over the sample period.

Comparing and Combining Two Approaches for Chance Constrained DEA

This paper presents a comparison of two different models (Land et al (1993) and Olesen and Petersen (1995)), both designed to extend DEA to the case of stochastic inputs and outputs. The two models constitute two approaches within this area, that share certain characteristics. However, the two models behave very differently, and the choice between these two models can be confusing. This paper presents a systematic attempt to point out differences as well as similarities. It is demonstrated that the two models under some assumptions do have Lagrangian duals expressed in closed form. Similarities and differences are discussed based on a comparison of these dual structures. Weaknesses of the each of the two models are discussed and a merged model that combines attractive features of each of the two models is proposed.

Far out or alone in the crowd: a taxonomy of peers in DEA

A method is presented for classifying strongly efficient units in DEA as interior or exterior, and as self-evaluators or active peers. The exterior strongly efficient units are found by running the enveloping procedure “from below”. There is no firm production-function evidence of the efficiency of exterior self-evaluators. Interior self-evaluators are more likely to have active peers as neighbours in more directions and may therefore represent technology. When performing a second stage regression analysis of efficiency scores, exterior self-evaluators should be removed. The proportion of exterior active peers also provides information on whether the variable specification is supported by the data.

The cost implications of waste reduction: factor demand, competitiveness and policy implications

Manufacturing produces both good and “bad” outputs, such as waste, which have negative environmental effects. Economic (e.g., tax) and non-economic (e.g., reputation) incentives encourage firms to reduce waste. However, such practices are costly because decreases in output produced or increases in inputs used may accompany waste reduction. We employ a cost function approach to evaluate patterns of output and waste production and capital, labor, and materials use, for UK manufacturing plants. We find that costs of waste reduction generally imply increasing materials use and capital and labor input saving, but vary by county, region, and industry.

Opening the black box: Finding the source of cost inefficiency

Parametric and nonparametric procedures are used to identify the apparent source of cost inefficiency in banking. Inefficiencies of 20–25% from earlier studies are reduced to 1–5% when, in addition to commonly specified cost function influences, variables reflecting banks’ external business environment and industry indicators of “productivity” are added. These productivity indicators explain most of the reduction in bank operating cost over 1992–2001 and was 5 times the reduction in the dispersion of inefficiency. Inefficiency appears stable over time because it is small relative to industry-wide cost changes occurring concurrently and because technology dispersion is imperfect.

Do we estimate an input or an output distance function? An application of the mixture approach to European railways

In this paper, we estimate parametric input and output distance functions and discuss how to estimate a mixture/latent class model (LCM) involving the output and input distance functions in the context of multi-input and multi-output production technology. The proposed technique is applied to a panel data on European Railways (1971–1994). This model allows us to identify determinants of the efficiency orientation, thereby providing useful information that can help researchers to choose between the input and the output-oriented approaches. In addition, we develop cross-indices that can be used to compute input (output) technical inefficiency from the estimates of output (input) distance function.